The Taub Faculty of Computer Science Events and Talks

We investigate the asymptotic rates of length-$n$ binary codes with VC-dimension at most $dn$ and minimum distance at least $\delta n$. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a shortening approach combining Sauer--Shelah lemma and the linear programming bound.

Two lower bounds are given using Gilbert--Varshamov type arguments over constant-weight and Markov-type sets.